There are three basic types of slugs in common use. The most common is the Foster-style slug. Available from all the major ammo-makers, the Foster slug resembles an inverted lead shot glass. It requires no "spin" to stabilize. It flys point-on for the same reason a badminton "birdie" does...most all the weight is at the nose.
The "sabot" slugs are smaller in diameter than the Foster style (usually around .50). They are usually "wasp-waisted" and are enclosed in two halves of a bore-sized plastic sleeve (the sabot). The sabot falls away after the slug exits the bore. Spin can be imparted to the sabot-style slugs by using a rifled barrel. This generally increases the accuracy with which the sabot slugs can be delivered. However, a rifled shotgun barrel will not pattern well with shot.
The last common type is the Rottweil/Brenneke slug. It is a solid lead projectile with a thick felt wad screwed to its base. It functions like the Foster slug, with the attached wad performing the same function that the thin skirt walls of the Foster slug...that is, ensuring that most of the projectile weight is forward, so it'll fly nose-first. The Brennekes, like the Foster, are best suited to smoothbores.